Illumination optical system and image projection apparatus

ABSTRACT

An illumination optical system include a first lens array including multiple lens cells that split a light beam emitted from a light source into multiple light beams, a second lens array including lens cells that the light beams split by the lens cells of the first lens array are incident thereon, and an optical element configured to illuminate an image display element by superposing light beams emerging from the second lens array on the image display element. At least one of the first lens array and the second lens array includes at least two lens cells each having a curved surface that is formed so as to be continuous with a curved surface of an adjacent lens cell, the at least two lens cells being decentered, and at least two lens cells of the first lens array have different radii of curvature.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an illumination optical systemincluding a lens array that splits a light beam emitted from a lightsource into multiple light beams and also relates to an image projectionapparatus including the illumination optical system.

2. Description of the Related Art

An illumination optical system heretofore known includes a first fly'seye lens, which splits a light beam emitted from a light source intomultiple light beams, and a second fly's eye lens, which includesmultiple lens cells corresponding to the first fly's eye lens, in orderto uniformly and efficiently illuminate an illumination surface of, forexample, a liquid crystal display element.

The English abstract of Japanese Patent Laid-Open No. 10-115870 (PatentDocument 1) discloses an illumination optical system in which decenteredlenses are adopted as lens cells that constitute a first fly's eye lensor a second fly's eye lens to improve parallelism of light beams andreduce the amount of light loss in the illumination optical system.

US 2003/0174294 (Patent Document 2) and the English abstract of JapanesePatent Laid-Open No. 2003-090981 (Patent Document 3) each disclose anillumination optical system in which thicknesses of lens cells, whichconstitute a first fly's eye lens or a second fly's eye lens, are madedifferent from one another in a stepwise manner in accordance with theiramounts of decentering so that curved surfaces of the decentered lenscells are substantially continuous with one another.

However, there is a problem with the technology disclosed in PatentDocument 1 in that a shadow is generated in an illumination area becausethe curved surfaces of the decentered lens cells are discontinuous andsteps exist between the decentered lens cells (FIG. 11A).

In the technologies disclosed in Patent Documents 2 and 3, thicknessesof the lens cells are made different from one another so that the curvedsurfaces of the decentered lens are continuous with one another.However, the technologies have a problem in that, by making thicknessesof the lens cells different, principal points of the lens cells aredisplaced in an optical axis direction and consequently split lightbeams do not converge at target convergent points (FIG. 11B).

When decentered lenses are adopted as the lens cells constituting thefirst fly's eye lens and curved surfaces of the lens cells arecontinuous with one another as illustrated in FIG. 12, positions atwhich split light beams split by the lens cells of the first fly's eyelens maximally converge are displaced from principal points of lenscells of the second fly's eye lens. The reference signs x in FIG. 12schematically indicate how much principal points of lens cells aredisplaced from a principal point of the lens cell on the optical axis ofthe illumination optical system, and how much focus points of splitlight beams from the lens cells are displaced from a focus point of asplit light beam from the lens cell on the optical axis. Due to thedisplacement, some of the split light beams that are supposed to beincident on the corresponding lens cells are unintentionally madeincident on adjacent lens cells and illuminate an area outside of aneffective area of a liquid crystal display element. Accordingly, someamount of light loss occurs.

SUMMARY OF THE INVENTION

The present invention provides an illumination optical system and animage projection apparatus including the same that can reduce the amountof light loss even when curved surfaces of decentered lens cells arecontinuous with one another.

In order to solve the above problems, the illumination optical systemaccording to the present invention is an illumination optical systemthat includes a first lens array including multiple lens cells thatsplit a light beam emitted from a light source into multiple lightbeams, a second lens array including lens cells that the light beamssplit by the lens cells of the first lens array are incident thereon,and an optical element configured to illuminate an image display elementby superposing light beams emerging from the second lens array on theimage display element. At least one of the first lens array and thesecond lens array includes at least two lens cells each having a curvedsurface that is formed so as to be continuous with a curved surface ofan adjacent lens cell, the at least two lens cells being decentered, andat least two lens cells of the first lens array have different radii ofcurvature.

Further features of the present invention will become apparent from thefollowing description of exemplary embodiments with reference to theattached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of an illumination optical systemaccording to a first embodiment of the present invention.

FIG. 2 illustrates a convergent point of a split light beam.

FIG. 3A illustrates an example of a decentered fly's eye lens accordingto an embodiment of the present invention, and FIG. 3B is a tableindicating properties of lens cells of the fly's eye lens.

FIGS. 4A and 4B illustrate convergent points of split light beams.

FIG. 5 is a schematic diagram of an illumination optical systemaccording to a second embodiment of the present invention.

FIGS. 6A to 6C each schematically illustrate a polarization conversionelement and a convergent point of a split light beam.

FIGS. 7A and 7B are schematic diagrams of an illumination optical systemaccording to a third embodiment of the present invention.

FIG. 8 is a schematic diagram of an illumination optical systemaccording to a fourth embodiment of the present invention.

FIG. 9 is a schematic diagram of an illumination optical systemaccording to a fifth embodiment of the present invention.

FIG. 10 is a schematic diagram of an image projection apparatusaccording to a sixth embodiment of the present invention.

FIGS. 11A and 11B are schematic diagrams of fly's eye lenses formed ofdecentered lens cells.

FIG. 12 is a schematic diagram of convergent points of split light beamsthat have passed through curved surfaces of decentered lens cells thatare continuous with one another.

FIG. 13 is a schematic diagram of an effective area of a second fly'seye lens.

FIG. 14 is a schematic diagram of an effective area of a polarizationconversion element.

DESCRIPTION OF THE EMBODIMENTS

Referring to the drawings, embodiments of the present invention will bedescribed in detail below.

First Embodiment

FIG. 1 is a schematic diagram illustrating an illumination opticalsystem according to a first embodiment of the present invention. FIG. 1illustrates a light source 1, a parabolic reflector 2, a converging lens8, a first fly's eye lens (first lens array) 9, a second fly's eye lens(second lens array) 10, a condenser lens (optical element) 6, and aliquid crystal display element (image display element) 7. The firstfly's eye lens 9 is formed by arranging rectangular lens cells, whichhave similar figures to the liquid crystal display element 7, in amatrix. The second fly's eye lens 10 includes multiple lens cellscorresponding to the lens cells of the first fly's eye lens 9.

Light emitted from the light source 1 is reflected by the parabolicreflector 2 and becomes substantially parallel light beams. Thesubstantially parallel light beams are incident on the converging lens 8and changed into converged light by the converging lens 8. The convergedlight is incident on the first fly's eye lens 9.

The lens cells constituting the first fly's eye lens 9 are decentered,and the amount by which the center of curvature is displaced from thecenter of each lens cell (referred to as a decentering amount, below)increases stepwise from a lens cell near the optical axis toward a lenscell in a peripheral portion. Furthermore, the thicknesses of the lenscells in the optical axis direction increase stepwise the closer a lenscell is disposed to a peripheral portion so that the curved surfaces ofthe lens cells are substantially continuous with one another.Accordingly, the principal points of the lens cells are displaced in atranslational manner further toward the light source the closer a lenscell is disposed to a peripheral portion. The first fly's eye lens as awhole has a recessed shape on the light source side, and a flat shape onthe second fly's eye lens side.

Note that the expression “a lens cell is decentered” herein refers to asituation where an optical axis of one lens cell (a straight lineconnecting centers of curvature of two surfaces of the lens cell) doesnot coincide with a line that passes through the center of the lens celland that is parallel to the optical axis. In this embodiment, lens cellsof the first fly's eye lens 9 other than a lens cell in the center aredecentered when viewed in the same direction as shown in FIG. 1 and in adirection that is parallel to the direction of FIG. 1.

Also note that the expression “curved surfaces are continuous with oneanother” herein refers to a situation where curved surfaces of adjacentlens cells are in contact with one another. In other words, curvedsurfaces of adjacent lens cells are joined to (or in contact with) oneanother at their ends (or ends of curved surfaces of adjacent lens cellsare positioned at the same position).

In the split light beam emerging from each lens cell of the first fly'seye lens 9, part of the light beam passing through the center of thelens cell becomes substantially parallel to the optical axis due todecentering of the lens cell. The split light beam converges to acorresponding one of the lens cells of the second fly's eye lens 10. Thesplit light beam maximally converges (is focused) around the secondfly's eye lens 10 and forms an image of the light source 1 thereon.After that, the light beam becomes divergent light again, is incident onthe condenser lens 6, and is superposed on the liquid crystal displayelement 7 by the condenser lens 6.

If all the lens cells of the first fly's eye lens 9 have the same radiusof curvature, generally, the positions at which split light beamsmaximally converge are displaced farther from effective areas (a rangeindicated by a in FIG. 1 or a shaded part in FIG. 13) of the lens cellsof the second fly's eye lens 10 the closer a lens cell of the firstfly's eye lens is disposed to a peripheral portion of the first fly'seye lens. Consequently, the widths of the split light beams in theeffective areas of the corresponding lens cells of the second fly's eyelens 10 increase, and a larger amount of light travels outside of theeffective areas of the corresponding lens cells of the second fly's eyelens 10. The parts of the light that are not incident on thecorresponding lens cells are condensed by the condenser lens 6 to aportion that is outside of an effective area of the liquid crystaldisplay element 7. Accordingly, an amount of light loss corresponding tothat of the parts of the light occurs. Note that FIG. 13 schematicallyillustrates a first lens array and a second lens array on the left, andillustrates a portion of the second lens array surrounded by the dottedline in an enlarged manner on the right.

The inventors of the present application have focused attention on thefact that the amount of the light beams travelling through the effectiveareas of the lens cells of the second fly's eye lens or effective areasof a polarization conversion element has to be increased to reduce theamount of light loss in the illumination optical system. Thus, theinventors have appropriately set the radius of curvature of each lenscell of the first fly's eye lens 9 such that the split light beamsmaximally converge in the effective areas of the lens cells of thesecond fly's eye lens 10.

In this embodiment, the radii of curvature of the lens cells of thefirst fly's eye lens 9 increase the closer a lens cell is disposed to aperipheral portion so that the split light beams maximally converge inthe effective areas of the lens cells of the second fly's eye lens 10.In other words, a lens cell that is disposed farther (further outward)from the optical axis has a larger radius of curvature than a lens cellthat is disposed on an inner side. To put it another way, the radii ofcurvature of the lens cells of the first fly's eye lens 9 are set suchthat paraxial split light beams that pass through the lens cells of thesecond fly's eye lens 10 have such widths that the light beams convergein the effective areas of the lens cells of the second fly's eye lens10.

Specifically, the radius of curvature of each lens cell of the firstfly's eye lens 9 is set such that a combined focal length of theconverging lens 8 and the lens cell of the first fly's eye lens 9increases by an amount equal to displacement of the principal point ofthe lens cell of the first fly's eye lens 9 (toward the liquid crystaldisplay element 7).

As described above, according to the embodiment of the presentinvention, an illumination optical system that reduces the amount oflight loss by appropriately setting the radii of curvature of thedecentered lens cells can be provided. The illumination optical systemaccording to the embodiment also has an effect of reducing theoccurrence of shadows in an illumination area since the curved surfacesof the lens cells are continuous with one another, and an effect ofimproving the yield in a process of producing the fly's eye lens.

Referring now to FIG. 2, the embodiment will be described further. FIG.2 illustrates a decentered lens cell C1 of the first fly's eye lens, alens cell C2 of the second fly's eye lens, and a line L1 that isperpendicular to the optical axis and passes through a point at whichthe center of the effective area of the lens cell C1 and the curvedsurface of the lens cell C1 cross each other. Part of the parallel lightbeam that is incident on the curved surface in a range of the line L1converges. The solid line indicates a split light beam emerging from thedecentered lens cell C1 in which the radius of curvature has not beenappropriately set. Here, the expression “the radius of curvature has notbeen appropriately set” refers to a situation where, for example, thelens cells of the first fly's eye lens are decentered lens cells, thecurved surfaces of the lens cells are continuous with one another, andall the lens cells have the same radius of curvature. If such a firstfly's eye lens is used, a split light beam emerging from the decenteredlens cell C1 maximally converges at a position that is far from aprincipal plane of the lens cell C2 as indicated by the solid line,although it is desirable that the split light beam maximally converge tothe principal plane.

In this embodiment, the lens cells of the first fly's eye lens aredecentered lens cells and the curved surfaces of the lens cells arecontinuous with one another. However, the radius of curvature of thedecentered lens cell C1 is made different from other lens cells so thatthe split light beam maximally converges at an appropriate position.

Here, the principal plane of the lens cell C2 of the second fly's eyelens 10 is taken as a datum position, and a position at which a splitlight beam split by a lens cell having a radius of curvature that hasnot been appropriately set maximally converges is denoted by Δ₁ withrespect to the datum position. The position Δ₁ takes a positive (+)value on a liquid crystal display element side in the optical axisdirection with respect to the datum position, and takes a negative (−)value on a light source side in the optical axis direction with respectto the datum position. When a convergent point of a split light beamemerging from each lens cell of the first fly's eye lens 9 according tothe embodiment is denoted by −A×Δ₁, it is preferable that the radii ofcurvature of the lens cells of the first fly's eye lens 9 be set suchthat a coefficient A falls within a range of the following expression(1):

0.5≦A1.5  (1).

When the expression (1) is satisfied, the split light beam is correctedas indicated by dotted lines in FIG. 2, so that the split light beammaximally converges at an appropriate position.

Although all the lens cells of the first fly's eye lens 9 may be set soas to satisfy the expression (1), the effect of the embodiment of thepresent invention can be obtained even when not all the lens cells areset so as to satisfy the expression (1).

It is considered that the amount of light loss is associated with awidth δ of a light beam in an effective area. Here, the width δ isexpressed in the following expression (2):

δ=|Δ₁ |·D/f  (2).

Here, D denotes an effective diameter of a lens cell of a first fly'seye lens 9, f denotes a focal length of the first fly's eye lens 9, and“·” is an operator indicating multiplication.

When the radius of curvature of the lens cell of the first fly's eyelens 9 is set appropriately so that Δ₁ becomes close to zero, the widthδ of the light beam in the effective area becomes close to zero and thusthe amount of light loss is reduced. On the other hand, when Δ₁ ischanged so as to be further away from zero, the width δ of the lightbeam in the effective area gradually increases and thus the amount oflight loss increases. In short, the coefficient A in the expression (1)denotes a degree to which a position at which a split light beammaximally converges is corrected.

Thus, even though the radii of curvature of the lens cells of the firstfly's eye lens 9 are individually changed, the degree to which theconvergent point Δ₁ of the split light beam is corrected can beprevented from being too small or too large as long as the width δ fallswithin a range that satisfies the expression (1). Thus, the amount oflight loss can be expected to be reduced well.

Preferably, the expression (3) below is satisfied:

δ/E1/10  (3).

Here, E denotes an effective area of a lens cell of the second fly's eyelens, and δ denotes the width of a light beam in the effective area.When the expression (3) is satisfied, the width δ of the light beamfalls within 10% of the size of the effective area and consequently aclear projection image can be produced. On the other hand, if the widthδ exceeds a range that satisfies the expression (1), the amount of lightis reduced. For this reason, it is preferable that the radii ofcurvature of the lens cells of the first fly's eye lens be set so as tosatisfy the expression (3).

More preferably, the expression (3a) below is satisfied:

δ/E≦1/20  (3a).

Still more preferably, the expression (3b) below is satisfied:

δ/E≈0  (3b).

When the expression (3b) is satisfied, A in the expression (1) isapproximately equal to 1.

The effect of reducing the amount of light loss can be obtained if atleast one of the lens cells that constitute the first and second fly'seye lenses is set to satisfy either the expression (1) or (3). It is,however, preferable that a larger number of lens cells or all the lenscells be set to satisfy the above expressions.

FIGS. 3A and 3B illustrate an example of lens cells of the first fly'seye lens having radii of curvature set with consideration of therefractive power of the converging lens 8. FIG. 3A is a schematicdiagram of the first fly's eye lens and FIG. 3B is a table including thethickness, focal length, and radius of curvature of each lens cellillustrated in FIG. 3A. Cell numbers in FIG. 3A correspond to cellnumbers in FIG. 3B. In the example illustrated in FIGS. 3A and 3B, theconverging lens 8 has a positive refractive power φ that is equal to0.01644. In the properties listed in the table of FIG. 3B, the radii ofcurvature of the lens cells of the first fly's eye lens are set in viewof the refractive power φ of the converging lens 8 and spacing betweenthe first fly's eye lens 9 and the second fly's eye lens such that thesplit light beams maximally converge at principal points of thecorresponding lens cells of the second fly's eye lens.

In a study performed by the inventors of the present application, it wasfound that, in the case where the radii of curvature are setindividually as illustrated in the table of FIG. 3B, illuminationefficiency is improved by approximately 2.0% compared to the case wherethe radii of curvature of all the lens cells are set to 28.29 mm, whichis the radius of curvature of lens cells adjacent to the optical axis inthe table of FIG. 3B.

As has been described above, if all the lens cells of the first fly'seye lens have the same radius of curvature, the convergent points of thesplit light beams are displaced from the effective areas of thecorresponding lens cells of the second fly's eye lens due to thedifference in thickness between the lens cells in the optical axisdirection, as illustrated in FIG. 4A. In contrast, when the radii ofcurvature of the lens cells of the first fly's eye lens areappropriately set, the light beams converge at appropriate positions andthe curved surfaces of the lens cells are continuous with one another.Accordingly, it is possible to provide an illumination optical systemthat can reduce the amount of light loss while the occurrence of shadowsin an illumination area is reduced and the yield of fly's eye lenses isimproved.

In the first embodiment, although it is only the first fly's eye lens 9that includes decentered lens cells, decentered lens cells may beincluded in the second fly's eye lens 10 instead, or may be included inboth the first fly's eye lens 9 and the second fly's eye lens 10.

In the structure according to the first embodiment, the converging lens8 having a positive refractive power and the parabolic reflector 2 aredisposed on a side that is closer to the light source 1 than the firstfly's eye lens 9. However, the present invention is also applicable to astructure that includes an elliptical reflector or a concave lens havinga negative refractive power. That is, the present invention isapplicable to any structure in which the radius of curvature of eachlens cell of the first fly's eye lens is set with consideration of therefractive power of all the optical elements, including a reflector,which are disposed on a side that is closer to the light source 1 thanthe first fly's eye lens 9 is.

If the condenser lens 6 is capable of superposing split light beams onthe liquid crystal display element, the condenser lens 6 may be aconcave mirror.

Not all the lens cells of the first fly's eye lens have to be formedsuch that the curved surfaces of the lens cells are continuous with oneanother. The present invention is applicable to any structure thatincludes a decentered lens cell, which has a curved surface that iscontinuous with curved surfaces of adjacent lens cells and which has aradius of curvature that is made different from those of other lenscells. Even in this structure, the effect of reducing the amount oflight loss can be obtained while the occurrence of shadows in projectionimages is reduced.

Second Embodiment

FIG. 5 is a schematic diagram illustrating an illumination opticalsystem according to a second embodiment of the present invention. Lightemitted from a light source 1 is reflected by a parabolic reflector 2and becomes substantially parallel light beams. The substantiallyparallel light beams are incident on a converging lens 8 and changedinto converged light by the converging lens 8. The converged light isincident on a first fly's eye lens 11 formed by arranging rectangularlens cells, which have similar figures to the liquid crystal displayelement 7, in a matrix.

Lens cells constituting the first fly's eye lens 11 are decentered, andthe decentering amounts increase stepwise from a lens cell near theoptical axis toward a lens cell in a peripheral portion. Furthermore,the thicknesses of the lens cells increase stepwise the closer a lenscell is disposed to a peripheral portion so that the curved surfaces ofthe lens cells are substantially continuous with one another.

In the split light beam that has been incident on each lens cell of thefirst fly's eye lens 11, part of the light beam passing through thecenter of the lens cell becomes substantially parallel to the opticalaxis due to decentering of the lens cell. The split light beam convergesat a position near the polarization conversion element 13. In FIG. 5, a1denotes an incident-side effective area of the polarization conversionelement 13 and a2 denotes an emerging-side effective area of thepolarization conversion element 13. Multiple split light beams thatconverge near the polarization conversion element 13 and diverge againare superposed on the liquid crystal display element 7 by the condenserlens 6.

FIG. 6A is a schematic diagram of the polarization conversion element13. The polarization conversion element 13 includes multiple prismaticpolarizing beam splitters and half-wave plates. Each polarizing beamsplitter has a polarization splitting film. The half-wave plates aredisposed on surfaces of every other polarizing beam splitter from whichlight beams emerge. In FIG. 6A, a1 denotes an incident-side distancebetween the polarization splitting film and a reflection film that areobliquely disposed at approximately 45 degrees with respect to theincident surface. Light that is incident on the polarization conversionelement 13 is split into P-polarized light and S-polarized light by thepolarization splitting film. The S-polarized light is reflected by theadjacent reflection film in the same direction as the P-polarized lighttravels, and is then emitted through a space between two adjacenthalf-wave plates. The P-polarized light split by the polarizationsplitting film is converted into S-polarized light by the half-waveplate disposed on the emerging surface and then emitted. In FIG. 6A, a2denotes an emerging-side distance between the polarization splittingfilm and the reflection film. In the above manner, unpolarized lightthat is incident on the polarization conversion element 13 is convertedinto S-polarized light. Here, the polarization conversion element 13 mayconvert light into P-polarized light.

As illustrated in FIGS. 6B and 6C, if a position at which a split lightbeam split by the first fly's eye lens maximally converges is outsidethe polarization conversion element 13, the width of the split lightbeam on the incident surface and the emerging surface of the polarizingbeam splitter increases excessively. If part of light beam travelsoutside of an effective area (shaded part in FIG. 14) of the polarizingbeam splitter having a width that is equivalent to that of one side ofthe polarizing beam splitter, P-polarized light that is supposed to beconverted into S-polarized light is emitted as it is without beingconverted to the S-polarized light, or S-polarized light is convertedinto unwanted P-polarized light and then emitted. As a result,efficiency in polarization conversion is reduced and the amount of lightloss is increased. FIG. 14 schematically illustrates a first lens array,a polarization conversion element, and incident light on the left, andillustrates an effective area of the polarizing beam splitter surroundedby the dotted line in an enlarged manner on the right.

As described in the first embodiment, light loss occurs not only in thepolarization conversion element 13. If parts of light beams emergingfrom lens cells of the first fly's eye lens 11 travel outside ofeffective areas of the corresponding lens cells of the second fly's eyelens 12, the parts of light beams result in light loss.

The thicknesses of the lens cells of the first fly's eye lens 11 in theoptical axis direction increase, the closer a lens cell is disposed to aperipheral portion. Accordingly, the principal points of lens cells ofthe first fly's eye lens 11 are displaced more in a translational mannertoward the light source, the closer a lens cell is disposed to aperipheral portion. If all the lens cells of the first fly's eye lens 11have the same radius of curvature, light beams maximally converge atpositions that are farther from the effective areas of the polarizationconversion element 13 the closer a lens cell is disposed to a peripheralportion. Consequently, the width of the split light beam in theeffective area increases, and light loss occurs.

Generally, the size of each effective area of the polarizationconversion element 13 is set to be approximately half the size of theeffective area of a corresponding lens cell of the second fly's eye lens12. As described in the first embodiment, the amount of light loss isdetermined by a ratio of the width δ of the split light beam to the sizeof the effective area. Accordingly, when the width of a light beam inthe effective area of the polarization conversion element 13 is the sameas the width of a light beam in the effective area of the lens cell ofthe second fly's eye lens 12, the amount of light loss becomes larger inthe effective area of the polarization conversion element 13.

For this reason, in this embodiment, the radii of curvature of the lenscells of the first fly's eye lens 11 are set such that the split lightbeams maximally converge to the corresponding effective areas of thepolarization conversion element 13. More specifically, the radii ofcurvature of lens cells of the first fly's eye lens 11 increase, thecloser a lens cell is disposed to a peripheral portion. In this manner,an illumination optical system that reduces an amount of light loss canbe provided. Furthermore, since the curved surfaces of the lens cells ofthe first fly's eye lens 11 are continuous with one another, theillumination optical system is capable of reducing the width of splitlight beams in the effective area while the occurrence of shadows in anillumination area is reduced and the yield of fly's eye lenses in aprocess of producing the fly's eye lenses is improved.

Now, an exemplary range of the radius of curvature will be described. Athickness of the polarization conversion element 13 in the optical axisdirection is denoted by d, and the position of an internal center d/2 ofthe polarization conversion element 13 in the optical axis direction istaken as a datum position. As described in the first embodiment, aposition at which a split light beam split by a lens cell having theradius of curvature being not appropriately set maximally converges isdenoted by Δ₂ with respect to the datum position, which is the internalcenter d/2. The position Δ₂ takes a positive value on the liquid crystaldisplay element side of the datum position in the optical axisdirection, and takes a negative value on the light source side of thedatum position in the optical axis direction. A position at which asplit light beam split by a lens cell of the first fly's eye lens 11according to the second embodiment having the radius of curvature beingappropriately set maximally converges is denoted by −B×Δ₂. Here, it isdesirable that the radius of curvature of a lens cell of the first fly'seye lens 11 be set such that a coefficient B satisfies the followingexpression (4):

0.5≦B≦1.5+(d/2)/Δ₂  (4).

As described in the first embodiment, it is considered that the amountof light loss is associated with a width δ of a light beam in aneffective area. Here, the width δ is expressed in the expression (5) asfollows:

δ=|Δ₂ |·D _(F) /f _(F)  (5).

Here, f_(F) denotes a combined focal length of the first and secondfly's eye lenses 11 and 12 and D_(F) denotes an effective diameter of alens cell of a first fly's eye lens 11.

When Δ₂ is set so as to be zero by changing the radii of curvature ofthe lens cell of the first fly's eye lens 11, the width δ of the lightbeam in the effective area becomes zero and thus the illuminationefficiency becomes the maximum. If the corrected position Δ₂, at whichthe split light beam emerging from a lens cell of the first fly's eyelens 11 having the appropriate radius of curvature maximally converges,is changed so as to be further away from zero, the width δ of the lightbeam in the effective area gradually increases, and thereby the amountof light loss increases. In short, the coefficient B denotes a degree ofcorrecting the position at which a split light beam maximally converges.

The polarization conversion element 13 according to the secondembodiment is different from the second fly's eye lens 10 according tothe first embodiment in that the polarization conversion element 13 haseffective areas on two sides, one on an incident side and the other onan emerging side. Considering that the amount of light loss of thepolarization conversion element 13 changes in association with thechange in Δ₂, a larger one of widths δ of a light beam in theincident-side effective area and emerging-side effective area of thepolarization conversion element 13 greatly affects the amount of lightloss. Now, the widths of a light beam in the incident-side andemerging-side effective areas of the polarization conversion element 13with respect to the datum position are considered. When the convergentpoint of the split light beam is displaced from the datum position inthe positive direction or toward the liquid crystal display element, thewidth of the light beam in the incident-side effective area increases,whereas the width of the light beam in the emerging-side effective areareduces. Here, almost all the amount of light loss due to the increasein width of the light beam in the incident-side effective area iscancelled.

For this reason, while the convergent point of the split light beamfalls within a range from the datum position of the polarizationconversion element 13 to a position that is a distance d/2 away from thedatum position in the positive direction, a substantially uniformillumination efficiency is obtained. Thus, a range in the secondembodiment in which the illumination efficiency is appropriatelyimproved is shifted by d/2 toward the liquid crystal display elementfrom that in the case of the first embodiment. In view of these facts,the expression (4) is obtained by using a change of a larger one of thewidths δ of a light beam on the incident side and emerging side withrespect to a change of Δ₂.

Even when the radii of curvature of the lens cells of the first fly'seye lens 11 are changed independently of other factors in a range thatsatisfies the expression (4), the degree of correcting the convergentpoint Δ₂ of the split light beam does not become too small or too large.Thus, sufficient illumination efficiency is expected.

In the second embodiment, it is only the first fly's eye lens 11 thatincludes decentered lens cells, but the second fly's eye lens 12 mayinclude decentered lens cells, instead. Alternatively, both the firstfly's eye lens 11 and the second fly's eye lens 12 may includedecentered lens cells.

Third Embodiment

FIGS. 7A and 7B illustrate schematic diagrams of an illumination opticalsystem according to a third embodiment of the present invention. FIG. 7Ais a schematic diagram of a first cross section (taken in the X-Zdirections in the drawing) and FIG. 7B is a schematic diagram of asecond cross section (taken in the Y-Z directions in the drawing). Thefirst and second cross sections are both taken along the optical axisdirection and are perpendicular to each other.

Light emitted from a light source 1 is reflected by a parabolicreflector 2 and becomes substantially parallel light beams. Thesubstantially parallel light beams are incident on a converging lens 8and changed into converged light by the converging lens 8. The convergedlight is incident on a first fly's eye lens 14.

Lens cells constituting the first fly's eye lens 14 are decentered, andthe decentering amounts increase stepwise from a lens cell near theoptical axis toward a lens cell in a peripheral portion. Furthermore,the thicknesses of the lens cells in the optical axis direction increasestepwise the closer a lens cell is disposed to a peripheral portion sothat the curved surfaces of the lens cells are substantially continuouswith one another.

In the split light beam emerging from each lens cell of the first fly'seye lens 14, part of the light beam passing through the center of thelens cell becomes substantially parallel to the optical axis due todecentering of the lens cell. The split light beam converges to acorresponding one of the lens cells of the second fly's eye lens 15. Themultiple split light beams emerging from the second fly's eye lens 15are superposed on the liquid crystal display element 7 by the condenserlens 6.

Now, the first cross section of FIG. 7A out of the two cross sectionstaken along the optical axis and being perpendicular to each other isreferred to. In the first cross section, polarization splitting films ofpolarizing beam splitters and half-wave plates of a polarizationconversion element 13 are arranged along the first cross section (in theX-Y directions). Here, the radii of curvature of the lens cells of thefirst fly's eye lens 14 should be set such that the split light beamsmaximally converge to effective areas of the polarization conversionelement 13.

If all the lens cells of the first fly's eye lens 14 have the sameradius of curvature, generally, the positions at which light beamsmaximally converge would be farther from the effective areas of thepolarization conversion element 13 the closer a lens cell of the firstfly's eye lens is disposed to a peripheral portion. Consequently, thewidth of the split light beams in the effective areas increases, andlight loss occurs.

Thus, in the third embodiment, the radii of curvature of the lens cellsof the first fly's eye lens 14 are set such that a lens cell that isdisposed closer to a peripheral portion has a larger radius of curvaturein order that the split light beams maximally converge in the effectiveareas of the polarization conversion element 13 in the first crosssection.

Now, the second cross section of FIG. 7B out of the two cross sectionstaken along the optical axis and being perpendicular to each other arereferred to. In the second cross section, no effect is observed for thepolarization splitting films of the polarizing beam splitters and thehalf-wave plates of the polarization conversion element 13 and there isno effective area as the one included in the first cross section. Here,the radii of curvature of the lens cells of the first fly's eye lens 14should be set such that the split light beams maximally converge toeffective areas of the lens cells of the second fly's eye lens 15.

If all the lens cells of the first fly's eye lens 14 have the sameradius of curvature, light beams maximally converge at positions thatare farther from the effective areas of the lens cells of the secondfly's eye lens 15 the closer a lens cell of the first fly's eye lens isdisposed to a peripheral portion. Consequently, the widths of the splitlight beams in the effective areas increase, and light loss occurs.

In the third embodiment, the radii of curvature of the lens cells of thefirst fly's eye lens 14 are set such that a lens cell that is disposedcloser to a peripheral portion has a larger radius of curvature in orderthat the split light beams maximally converge in the effective areas ofthe lens cells of the second fly's eye lens 15 in the second crosssection.

As has been described above, it is possible to provide an illuminationoptical system that can reduce the amount of light loss. To be morespecific, the amount of light loss can be reduced by reducing the widthsof split light beams in corresponding effective areas while theoccurrence of shadows in an illumination area is reduced and the yieldof fly's eye lenses in a process of producing the fly's eye lenses isimproved.

By focusing on the fact that convergent points of a split light beamthat affect reduction of the amount of light loss are different fordifferent cross sections, another effect of reducing the amount of lightloss can be obtained in the third embodiment by forming a decenteredlens cell that has different radii of curvature for the first and secondcross sections.

In the third embodiment, it is only the first fly's eye lens 14 thatincludes decentered lens cells, but the second fly's eye lens 15 mayinclude decentered lens cells, instead. Alternatively, both the firstfly's eye lens 14 and the second fly's eye lens 15 may includedecentered lens cells.

Even in a case where a lens cell has different decentering amountsbetween the first and second cross sections, the above effects of theembodiment can be obtained.

Fourth Embodiment

FIG. 8 is a schematic diagram illustrating an illumination opticalsystem according to a fourth embodiment of the present invention. Lightemitted from a light source 1 is reflected by a parabolic reflector 2and becomes substantially parallel light beams. The substantiallyparallel light beams are incident on a converging lens 8 and changedinto converged light by the converging lens 8. The converged light isincident on a first fly's eye lens 16.

Lens cells constituting the first fly's eye lens 16 are decentered, andthe decentering amounts increase stepwise from a lens cell near theoptical axis toward a lens cell in a peripheral portion. Furthermore,the thicknesses of the lens cells in the optical axis direction increasestepwise the closer a lens cell is disposed to a peripheral portion sothat the curved surfaces of the lens cells are substantially continuouswith one another.

Curved surfaces of the lens cells constituting first fly's eye lens 16face a second fly's eye lens 17. Distances between lens cells of thefirst fly's eye lens 16 and corresponding lens cells of the second fly'seye lens 17 reduce stepwise, the closer a lens cell of the first fly'seye lens 16 is disposed to a peripheral portion from the center of theoptical axis.

In the split light beam that has been incident on and split by each lenscell of the first fly's eye lens 16, part of the light beam passingthrough the center of the lens cell becomes substantially parallel tothe optical axis due to decentering of the lens cell. The split lightbeam converges to a corresponding one of the lens cells of the secondfly's eye lens 17.

The multiple split light beams emerging from the second fly's eye lens17 are superposed on a liquid crystal display element 7 by a condenserlens 6.

If all the lens cells of the first fly's eye lens 16, from the one nearthe optical axis to the one near a peripheral portion, have the sameradius of curvature, the split light beams maximally converge atpositions that are farther from the effective areas of the lens cells ofthe second fly's eye lens 15 the closer a lens cell of the first fly'seye lens 16 is disposed to a peripheral portion. Consequently, thewidths of the split light beams in the effective areas increase, andillumination efficiency is reduced.

In the fourth embodiment, the radii of curvature of the lens cells ofthe first fly's eye lens 16 are set such that a lens cell that isdisposed closer to a peripheral portion has a smaller radius ofcurvature in order that the split light beams maximally converge in theeffective areas of the lens cells of the second fly's eye lens 17. Inother words, the radius of curvature of at least two lens cells of thefirst fly's eye lens 16 is set such that a split light beam forms animage of the light source 1 between, in the optical axis direction ofthe lens cell, a surface vertex of a curved surface of a correspondingone of the lens cells of the second fly's eye lens 17 and a contactpoint at which the corresponding lens cell of the second fly's eye lens17 is in contact with an adjacent lens cell. With this setting, thewidth of the split light beam in the effective area can be reduced, andthus illumination efficiency can be improved.

Here, a split light beam forms an image of the light source 1 at aposition at which the light beam maximally converges, and the imagingmagnification thereof is proportional to the focal length of the firstfly's eye lens 16. In the forth embodiment, the radii of curvature ofthe lens cells of the first fly's eye lens 16 are smaller or the focallengths of the lens cells of the first fly's eye lens 16 are shorter thecloser a lens cell is disposed to a peripheral portion. Thus, theimaging magnification at which lens cells of the first fly's eye lens 16form images of the light source 1 is smaller than in the case where allthe lens cells have the same radius of curvature. That is, in the fourthembodiment, an effect of reducing the width of a light beam in aneffective area is obtained not only by appropriately setting the radiiof curvature but also by reducing the imaging magnification at which animage of the light source 1 is formed.

As has been described above, it is possible to provide an illuminationoptical system that can improve illumination efficiency. To be morespecific, illumination efficiency can be improved by reducing the widthsof split light beams in corresponding effective areas while theoccurrence of shadows in an illumination area is reduced and the yieldof fly's eye lenses in a process of producing the fly's eye lenses isimproved.

Fifth Embodiment

FIG. 9 is a schematic diagram illustrating an illumination opticalsystem according to a fifth embodiment of the present invention. Lightemitted from a light source 1 is reflected by a parabolic reflector 2and becomes substantially parallel light beams. The substantiallyparallel light beams are incident on a converging lens 8 and changedinto converged light by the converging lens 8. The converged light isincident on a first fly's eye lens 18.

Lens cells constituting the first fly's eye lens 18 are decentered, andthe decentering amounts increase stepwise from a lens cell near theoptical axis toward a lens cell in a peripheral portion. Furthermore,the thicknesses of the lens cells in the optical axis direction increasestepwise the closer a lens cell is disposed to a peripheral portion sothat the curved surfaces of the lens cells are substantially continuouswith one another.

Curved surfaces of the lens cells constituting the first fly's eye lens18 face a second fly's eye lens 19. Distances between the lens cells ofthe first fly's eye lens 16 and the corresponding lens cells of thesecond fly's eye lens 17 reduce stepwise, the closer a lens cell isdisposed to a peripheral portion from the center of the optical axis.

In the split light beam that has been incident on and split by each lenscell of the first fly's eye lens 18, part of the light beam passingthrough the center of the lens cell becomes substantially parallel tothe optical axis due to decentering of the lens cell. The split lightbeam converges to a corresponding effective area of a polarizationconversion element 13.

The multiple split light beams emerging from the polarization conversionelement 13 are superposed on a liquid crystal display element 7 by acondenser lens 6.

If all the lens cells of the first fly's eye lens 18 have the sameradius of curvature, light beams maximally converge at positions thatare farther from the effective areas of the polarization conversionelement 13 the closer a lens cell of the first fly's eye lens 18 isdisposed to a peripheral portion. Consequently, the width of the splitlight beams in the effective areas increases, and illuminationefficiency is reduced.

In the fifth embodiment, the radii of curvature of the lens cells of thefirst fly's eye lens 18, from the one near the center of the opticalaxis to the one in a peripheral portion, are set such that a lens cellthat is disposed closer to a peripheral portion has a smaller radius ofcurvature in order that the split light beams maximally converge in theeffective areas of the polarization conversion element 13. With thissetting, the width of the split light beams in the effective areas canbe reduced, and thus illumination efficiency can be improved.

Here, a split light beam forms an image of the light source 1 at aposition at which the light beam maximally converges, and the imagingmagnification thereof for the case where the split light beam forms animage via a second fly's eye lens 19 is proportional to a combined focallength of the first and second fly's eye lenses 18 and 19. The combinedfocal length f_(F) of the first and second fly's eye lenses 18 and 19 isdetermined by the following expression (6):

f _(F) =f ₁ ×f ₂ /{f ₁ +f ₂−(L−α)}  (6).

Here, f₁ and f₂ respectively denote the focal lengths of the first andsecond fly's eye lenses. L denotes a distance between principal pointsof a lens cell of the first fly's eye lens and a corresponding lens cellof the second fly's eye lens for the case where the lens cells are notsubjected to thickness correction, the distance being caused due todecentering. In addition, α denotes an amount of change in distancebetween the lens cells, the amount of change being caused by thethickness correction. Each reference character denotes a generalizedrelationship for a combination of lens cells of the first and secondfly's eye lenses and is not limited to a specific combination of lenscells.

Generally, a focal length f₂ of the second fly's eye lens is assigned toa distance between lens cells. Thus, the expression (6) is changed to:

f _(F) =f ₁ ×f ₂ /{f ₁ +f ₂−(f₂−α)}=f ₁/(f₁+α)×f ₂  (7).

In the fifth embodiment, the radii of curvature of the lens cells of thefirst fly's eye lens 18 are smaller or the focal lengths f₁ of the lenscells of the first fly's eye lens 18 are shorter the closer a lens cellis disposed to a peripheral portion. The focal length f₁ is changed byreducing the coefficient f₁/(f₁+α) of f₂ in the expression (7), in sucha direction that a combined focal length is reduced. Thus, an image ofthe light source 1 formed by the lens cells of the first and secondfly's eye lenses becomes smaller than in the case where all the lenscells have the same radius of curvature. That is, in the fifthembodiment, an effect of reducing the width of a light beam in aneffective area is obtained not only by correcting the distance betweenthe position of the effective area and the position at which a splitlight beam maximally converges but also by reducing the imagingmagnification at which an image of the light source 1 is formed.

As has been described above, it is possible to provide an illuminationoptical system that can improve illumination efficiency. To be morespecific, illumination efficiency can be improved by reducing the widthsof split light beams in corresponding effective areas while theoccurrence of shadows in an illumination area is reduced and the yieldof fly's eye lenses in a process of producing the fly's eye lenses isimproved.

In the fifth embodiment, even if the radii of curvature of the lenscells of the first fly's eye lens increase stepwise from a lens cellnear the optical axis toward a lens cell in a peripheral portion, thesame effects will be obtained.

Sixth Embodiment

FIG. 10 is a schematic diagram illustrating an image projectionapparatus using the illumination optical system according to the firstembodiment. FIG. 10 illustrates a light source 1, a parabolic reflector2, a converging lens 8, a first fly's eye lens 9, a second fly's eyelens 10, a condenser lens (optical element) 6, a liquid crystal displayelement 7, a polarizing beam splitter 20, and a projection lens (opticalprojecting unit) 21. The first fly's eye lens 9 is formed by arrangingrectangular lens cells, which have similar figures to the liquid crystaldisplay element 7, in a matrix. The second fly's eye lens 10 includesmultiple lens cells corresponding to the lens cells of the first fly'seye lens 9.

In the sixth embodiment, a liquid crystal display element of areflective type is employed. The liquid crystal display element 7 isefficiently illuminated by the illumination optical system according tothe first embodiment. Here, the polarizing beam splitter 20 that isdisposed in front of the reflective liquid-crystal display panel 7allows only a P-polarized component of light emitted from the lightsource 1 to pass therethrough to the reflective liquid-crystal displaypanel 7. An S-polarized component of the light having its polarizingstate controlled by the reflective liquid-crystal display panel 7 isreflected by the polarizing beam splitter 20 and projected by theprojection lens 21 on a projection plane (screen) in an enlarged manner.

Here, a polarization conversion element may be disposed to the rear ofthe second fly's eye lens 10 to improve illumination efficiency.Furthermore, the liquid crystal display element is not limited to thereflective liquid crystal display element, and may be a transmissionliquid crystal display element, instead.

As described above, according to the first to sixth embodiments of thepresent invention, since the radii of curvature of decentered lens cellsare appropriately set, the amount of light loss can be reduced.

Among differences between positions of surface vertices of any two lenscells of the first fly's eye lens according to the embodiments of thepresent invention, the largest difference is denoted by gap_(max). Amongdistances between surface vertices of lens cells of the first fly's eyelens and corresponding lens cells of the second fly's eye lens, theshortest distance is denoted by L_(min). Here, in order to sufficientlyimprove illumination efficiency as an effect obtainable in theembodiments, it is preferable that gap_(max)>L_(min)/20 be satisfied.

It is more preferable that L_(min)/5>gap_(max)>L_(min)/20 be satisfied.

A difference, in the optical axis direction, between focus points (atwhich the diameter of a light beam is the smallest) of any two lenscells of the first fly's eye lens according to the embodiments of thepresent invention is denoted by f_(gap). Here, it is preferable thatf_(gap)<L_(min)/10 be satisfied. In other words, it is preferable thatf_(gap) not include the largest one of the differences between focuspoints of any two lens cells of the first fly's eye lens. It is morepreferable that f_(gap)<L_(min)/20 be satisfied.

Furthermore, in FIGS. 1, 7B, 8, and 10, an average of distances, in theoptical axis direction, between focus points of the lens cells of thefirst fly's eye lens and surface vertices of the corresponding lenscells of the second fly's eye lens is denoted by d1_(ave). Here, it ispreferable that d1_(ave)<L_(min)/10 be satisfied. It is more preferablethat d1_(ave)<L_(min)/20 be satisfied.

The largest one of the distances, in the optical axis direction, betweenfocus points of the lens cells of the first fly's eye lens and surfacevertices of the corresponding lens cells of the second fly's eye lens isdenoted by d1_(max). Here, it is preferable that d1_(max)<L_(min)/5 besatisfied. It is more preferable that d1_(max)<L_(min)/10 be satisfied.

In FIGS. 5, 7A, and 9, an average of distances, in the optical axisdirection, between focus points of the lens cells of the first andsecond fly's eye lenses and corresponding positions of the polarizationconversion element on the center line (indicated by dotted lines inFIGS. 6B and 6C, for example) in the optical axis direction is denotedby d2_(ave). Here, it is preferable that d2_(ave)<L_(min)/10 besatisfied. It is more preferable that d2_(ave)<L_(min)/20 be satisfied.

The largest one of distances, in the optical axis direction, betweenfocus points of the lens cells of the first and second fly's eye lensesand corresponding positions of the polarization conversion element onthe center line (indicated by dotted lines in FIGS. 6B and 6C, forexample) in the optical axis direction is denoted by d2_(max). Here, itis preferable that d2_(max)<L_(min)/5 be satisfied. It is morepreferable that d2_(max)<L_(min)/10 be satisfied.

In the above inequalities, each position of the polarization conversionelement on the center line in the optical axis direction may beinterchanged with a position at which part of a light beam passingthrough the center of the second fly's eye lens in parallel to theoptical axis is incident on a polarization splitting film of thepolarization conversion element (a position at which a light path of thepart of the light beam and the polarization splitting film intersectwith each other).

In the first and second embodiments, a fly's eye lens has a structure inwhich lens cells are arranged such that the radii of curvature of thelens cells are symmetric with respect to a first axis that crosses theoptical axis and that is parallel to the y axis. However, the presentinvention is not limited to this structure, and the radii of curvatureof the lens cells may be asymmetric with respect to the first axis. Inaddition, the radii of curvature of the lens cells may be asymmetricwith respect to a second axis that crosses the optical axis and that isparallel to the x axis.

In the first and second embodiments, a fly's eye lens having lens cellstwo-dimensionally arranged is described. However, the effect of reducingthe amount of light loss can be obtained even by adopting aone-dimensional cylindrical fly's eye lens. In this case, it is onlyrequired, for example, to set the radii of curvature of two cylindricallenses in a cylindrical lens array such that split light beams convergeat appropriate positions.

In addition, not all the lens cells in half an area that is divided bythe first axis or second axis have to have different radii of curvature.The amount of light loss can be reduced as long as the radii ofcurvature of at least two lens cells are appropriately set.

In another embodiment, a second lens array may include decentered lenscells. If the second lens array includes decentered lens cells andcurved surfaces of the lens cells are continuous with one another,principal points of the lens cells are displaced in accordance withdecentered shapes. For example, if the lens cells each have a decenteredshape such that the lens cell has a flat surface on the light sourceside and a concave surface on the liquid crystal display element side, aprincipal point of a lens cell that is disposed farther from the opticalaxis is displaced closer to the liquid crystal display element. On theother hand, if the lens cells each have a decentered shape such thateach lens cell has a flat surface on the light source side and a convexsurface on the liquid crystal display element side, a principal point ofa lens cell that is disposed farther from the optical axis is displacedcloser to the light source. Even in this embodiment, the effects of theother embodiments can be obtained by making two lens cells of the firstlens array have different radii of curvature so that light beamsmaximally converge to principal planes of the lens cells of the secondlens array. In other words, the decentering amounts of lens cells of thefirst lens array can be set such that split light beams split by thefirst lens array maximally converge at positions on or around theprincipal planes of the decentered lens cells of the second lens array.For example, an illumination optical system may be employed thatincludes, in order from the light source side, an elliptical reflector,a negative lens, a first lens array, and a second fly's eye lens, thefirst lens array having a convex surface on the light source side and aflat surface on the liquid crystal display element side, and the secondfly's eye lens having a flat surface on the light source side and aconcave surface on the liquid crystal display element side. Even in thiscase, the effects of the other embodiments can be obtained by making twolens cells of the first lens array have different radii of curvature sothat split light beams maximally converge to principal planes of thelens cells of the second lens array.

In another embodiment, lens cells of a first lens array are decenteredin a direction that is opposite to the direction in which the lens cellsof the first lens array according to the first embodiment aredecentered, and a polarization conversion element is disposed on a sidethat is closer to the liquid crystal display element than the first lensarray is. In this case, the lens cells are decentered such that a lenscell disposed on the outer side of the first lens array is decentered toa larger degree toward a light axis of the illumination optical systemthan a lens cell on the inner side of the first lens array. In otherwords, this is the case where the center of curvature of a curvedsurface of the outer lens cell is shifted toward the light axis of theillumination optical system with respect to the middle position of apitch of the lens cell, to a larger degree than the inner lens cell. Inthis case, the thickness of the outer lens cell needs to be smaller thanthat of the inner lens cell so that curved surfaces of adjacent lenscells are continuous with one another. Here, a distance between theprincipal planes of outer lens cells of the first and second lens arraysis smaller than a distance between the principal planes of inner lenscells of the first and second lens arrays. In this embodiment of thepresent invention, among at least two lens cells in the first lens arrayeach having a curved surface that is continuous with curved surfaces ofadjacent lens cells, an outer lens cell that is disposed further outwardfrom the optical axis of the illumination optical system has a smallerradius of curvature than an inner lens cell that is disposed closer tothe optical axis. With this setting, convergent points of split lightbeams emerging from the at least two lens cells are made less likely tobe displaced due to decentering of lens cells of the first lens array.Accordingly, illumination efficiency can be improved.

In another embodiment, a first lens array includes no decentered lenscell and a second lens array includes at least two lens cells eachhaving a curved surface that is continuous with curved surfaces ofadjacent lens cells. Even in this embodiment, an effect of improvingillumination efficiency can be obtained by making the radii of curvatureof at least two lens cells of the first lens array different from eachother such that split light beams maximally converge to principal planesof lens cells of the second lens array.

Although the embodiments of the present inventions have been describedthus far, the present invention is not limited to these embodiments.Various changes and modification can be made or embodiments can becombined within a scope of the gist of the invention.

While the present invention has been described with reference toexemplary embodiments, it is to be understood that the invention is notlimited to the disclosed exemplary embodiments. The scope of thefollowing claims is to be accorded the broadest interpretation so as toencompass all such modifications and equivalent structures andfunctions.

This application claims the benefit of Japanese Patent Application No.2011-089374 filed Apr. 13, 2011 and No. 2012-033155 filed Feb. 17, 2012,which are hereby incorporated by reference herein in their entirety.

1. An illumination optical system comprising: a first lens array including a plurality of lens cells that split a light beam emitted from a light source into a plurality of light beams; a second lens array including lens cells on which the light beams split by the lens cells of the first lens array are incident; and an optical element configured to illuminate an image display element by superposing light beams emerging from the second lens array on the image display element, wherein at least one of the first lens array and the second lens array includes at least two lens cells each having a curved surface that is formed so as to be continuous with a curved surface of an adjacent lens cell, the at least two lens cells being decentered, and wherein, in a cross section in which the at least two lens cells are decentered, at least two lens cells of the first lens array have different radii of curvature.
 2. The illumination optical system according to claim 1, wherein the first lens array includes the at least two lens cells each having a curved surface that is formed so as to be continuous with a curved surface of an adjacent lens cell, the at least two lens cells being decentered, and wherein in a cross section in which the at least two lens cells are decentered, the at least two lens cells have different radii of curvature.
 3. The illumination optical system according to claim 1, wherein among the at least two lens cells having different radii of curvature, a lens cell that is disposed farther from an optical axis of the second lens array has a larger radius of curvature than that of a lens cell that is disposed closer to the optical axis of the second lens array.
 4. The illumination optical system according to claim 2, wherein the radii of curvature of the at least two lens cells having different radii of curvature are set such that light beams split by the at least two lens cells each form an image of the light source between, in an optical axis direction of the lens cell, a surface vertex of a curved surface of a corresponding one of the lens cells of the second lens array and a contact point at which the corresponding lens cell is in contact with an adjacent lens cell.
 5. The illumination optical system according to claim 1, wherein the radii of curvature of the at least two lens cells having different radii of curvature are set such that light beams split by the at least two lens cells each maximally converge at a principal plane of a corresponding one of the lens cells of the second lens array.
 6. The illumination optical system according to claim 1, wherein each of the lens cells of the first lens array is decentered.
 7. The illumination optical system according to claim 1, wherein the first lens array has a concave surface on a light source side.
 8. The illumination optical system according to claim 1, further comprising: a polarization conversion element that polarizes the light beams emerging from the second lens array to a uniform polarization direction, wherein the radii of curvature of the at least two lens cells having different radii of curvature are set such that light beams split by the at least two lens cells maximally converge inside the polarization conversion element.
 9. The illumination optical system according to claim 8, wherein, when the center of the polarization conversion element in a thickness direction, which is an optical axis direction of the illumination optical system, is taken as a datum position, the radii of curvature of the at least two lens cells having different radii of curvature are set such that the light beams split by the at least two lens cells maximally converge at the datum position.
 10. The illumination optical system according to claim 8, wherein, when a cross section taken in a direction in which a plurality of polarization splitting films of the polarization conversion element are arranged is taken as a first cross section and a cross section that is taken along an optical axis of the illumination optical system and that is perpendicular to the first cross section is taken as a second cross section, a position at which the light beam split by each of the at least two lens cells maximally converges in the second cross section is closer to the light source than a position at which the light beam split by each of the at least two lens cells maximally converges in the first cross section.
 11. The illumination optical system according to claim 10, wherein radii of curvature of the at least two lens cells in the second cross section are smaller than radii of curvature of the at least two lens cells in the first cross section.
 12. An image projection apparatus comprising: an illumination optical system configured to illuminate an image display element with light emitted from an light source; and a projecting optical system configured to project an image formed by the image display element on a projection plane, wherein the illumination optical system includes a first lens array including a plurality of lens cells that split a light beam emitted from the light source into a plurality of light beams, a second lens array including lens cells on which the light beams split by the lens cells of the first lens array are incident, and an optical element configured to illuminate the image display element by superposing light beams emerging from the second lens array on the image display element, wherein at least one of the first lens array and the second lens array includes at least two lens cells each having a curved surface that is formed so as to be continuous with a curved surface of an adjacent lens cell, the at least two lens cells being decentered, and wherein, in a cross section in which the at least two lens cells are decentered, at least two lens cells of the first lens array have different radii of curvature. 